Fix advanced usage guide (#1785)

Author: devmotion

docs/src/using-turing/advanced.md

@@ -20,8 +20,7 @@ First, define a type of the distribution, as a subtype of a corresponding distri
 
 
 ```julia
-struct CustomUniform <: ContinuousUnivariateDistribution
-end
+struct CustomUniform <: ContinuousUnivariateDistribution end
 ```
 
 ### 2. Implement Sampling and Evaluation of the log-pdf
@@ -31,8 +30,11 @@ Second, define `rand` and `logpdf`, which will be used to run the model.
 
 
 ```julia
-Distributions.rand(rng::AbstractRNG, d::CustomUniform) = rand(rng) # sample in [0, 1]
-Distributions.logpdf(d::CustomUniform, x::Real) = zero(x)          # p(x) = 1 → logp(x) = 0
+# sample in [0, 1]
+Distributions.rand(rng::AbstractRNG, d::CustomUniform) = rand(rng)
+
+# p(x) = 1 → logp(x) = 0
+Distributions.logpdf(d::CustomUniform, x::Real) = zero(x)
 ```
 
 ### 3. Define Helper Functions
@@ -72,20 +74,10 @@ and then we can call `rand` and `logpdf` as usual, where
 
 To read more about Bijectors.jl, check out [the project README](https://github.com/TuringLang/Bijectors.jl).
 
-#### 3.2 Vectorization Support
-
-
-The vectorization syntax follows `rv ~ [distribution]`, which requires `rand` and `logpdf` to be called on multiple data points at once. An appropriate implementation for `Flat` is shown below.
-
-
-```julia
-Distributions.logpdf(d::Flat, x::AbstractVector{<:Real}) = zero(x)
-```
-
 ## Update the accumulated log probability in the model definition
 
 Turing accumulates log probabilities internally in an internal data structure that is accessible through
-the internal variable `_varinfo` inside of the model definition (see below for more details about model internals).
+the internal variable `__varinfo__` inside of the model definition (see below for more details about model internals).
 However, since users should not have to deal with internal data structures, a macro `Turing.@addlogprob!` is provided
 that increases the accumulated log probability. For instance, this allows you to
 [include arbitrary terms in the likelihood](https://github.com/TuringLang/Turing.jl/issues/1332)
@@ -123,19 +115,21 @@ end
 Note that `@addlogprob!` always increases the accumulated log probability, regardless of the provided
 sampling context. For instance, if you do not want to apply `Turing.@addlogprob!` when evaluating the
 prior of your model but only when computing the log likelihood and the log joint probability, then you
-should [check the type of the internal variable `_context`](https://github.com/TuringLang/DynamicPPL.jl/issues/154)
+should [check the type of the internal variable `__context_`](https://github.com/TuringLang/DynamicPPL.jl/issues/154)
 such as
 
 ```julia
-if !isa(_context, Turing.PriorContext)
+if DynamicPPL.leafcontext(__context__) !== Turing.PriorContext()
     Turing.@addlogprob! myloglikelihood(x, μ)
 end
 ```
 
 ## Model Internals
 
 
-The `@model` macro accepts a function definition and rewrites it such that call of the function generates a `Model` struct for use by the sampler. Models can be constructed by hand without the use of a macro. Taking the `gdemo` model as an example, the macro-based definition
+The `@model` macro accepts a function definition and rewrites it such that call of the function generates a `Model` struct for use by the sampler.
+Models can be constructed by hand without the use of a macro.
+Taking the `gdemo` model as an example, the macro-based definition
 
 ```julia
 using Turing
@@ -152,41 +146,36 @@ end
 model = gdemo([1.5, 2.0])
 ```
 
-is equivalent to the macro-free version
+can be implemented also (a bit less generally) with the macro-free version
 
 ```julia
 using Turing
 
 # Create the model function.
-function modelf(rng, model, varinfo, sampler, context, x)
-    # Assume s has an InverseGamma distribution.
-    s² = Turing.DynamicPPL.tilde_assume(
-        rng,
+function gdemo(model, varinfo, context, x)
+    # Assume s² has an InverseGamma distribution.
+    s², varinfo = DynamicPPL.tilde_assume!!(
         context,
-        sampler,
         InverseGamma(2, 3),
-        Turing.@varname(s),
-        (),
+        Turing.@varname(s²),
         varinfo,
     )
 
     # Assume m has a Normal distribution.
-    m = Turing.DynamicPPL.tilde_assume(
-        rng,
+    m, varinfo = DynamicPPL.tilde_assume!!(
         context,
-        sampler,
         Normal(0, sqrt(s²)),
         Turing.@varname(m),
-        (),
         varinfo,
     )
 
     # Observe each value of x[i] according to a Normal distribution.
-    Turing.DynamicPPL.dot_tilde_observe(context, sampler, Normal(m, sqrt(s²)), x, varinfo)
+    DynamicPPL.dot_tilde_observe!!(context, Normal(m, sqrt(s²)), x, Turing.@varname(x), varinfo)
 end
+gdemo(x) = Turing.Model(:gdemo, gdemo, (; x))
 
 # Instantiate a Model object with our data variables.
-model = Turing.Model(modelf, (x = [1.5, 2.0],))
+model = gdemo([1.5, 2.0])
 ```
 
 ## Task Copying